Abstract
Let R be a prime ring and set [x, y]1 = [x, y] = xy - yx for x, y ∈ R and inductively [x, y]k = [[x, y]k-1, y] for k > 1. We apply the theory of generalized polynomial identities with automorphisms and skew derivations to obtain the following result: If δ is a nonzero σ-derivation of R and L is a noncommutative Lie ideal of R so that [δ(x), x]k = 0 for all x ∈ L, where k is a fixed positive integer, then charR = 2 and for some field F. This result generalizes the case of derivations by Lanski and also the case of automorphisms by Mayne.
| Original language | English |
|---|---|
| Pages (from-to) | 259-270 |
| Number of pages | 12 |
| Journal | Monatshefte fur Mathematik |
| Volume | 158 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2009 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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An engel condition with skew derivations. / Chou, Ming Chu; Liu, Cheng Kai.
In: Monatshefte fur Mathematik, Vol. 158, No. 3, 01.01.2009, p. 259-270.Research output: Contribution to journal › Article
TY - JOUR
T1 - An engel condition with skew derivations
AU - Chou, Ming Chu
AU - Liu, Cheng Kai
PY - 2009/1/1
Y1 - 2009/1/1
N2 - Let R be a prime ring and set [x, y]1 = [x, y] = xy - yx for x, y ∈ R and inductively [x, y]k = [[x, y]k-1, y] for k > 1. We apply the theory of generalized polynomial identities with automorphisms and skew derivations to obtain the following result: If δ is a nonzero σ-derivation of R and L is a noncommutative Lie ideal of R so that [δ(x), x]k = 0 for all x ∈ L, where k is a fixed positive integer, then charR = 2 and for some field F. This result generalizes the case of derivations by Lanski and also the case of automorphisms by Mayne.
AB - Let R be a prime ring and set [x, y]1 = [x, y] = xy - yx for x, y ∈ R and inductively [x, y]k = [[x, y]k-1, y] for k > 1. We apply the theory of generalized polynomial identities with automorphisms and skew derivations to obtain the following result: If δ is a nonzero σ-derivation of R and L is a noncommutative Lie ideal of R so that [δ(x), x]k = 0 for all x ∈ L, where k is a fixed positive integer, then charR = 2 and for some field F. This result generalizes the case of derivations by Lanski and also the case of automorphisms by Mayne.
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UR - http://www.scopus.com/inward/citedby.url?scp=70350367994&partnerID=8YFLogxK
U2 - 10.1007/s00605-008-0043-5
DO - 10.1007/s00605-008-0043-5
M3 - Article
AN - SCOPUS:70350367994
VL - 158
SP - 259
EP - 270
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
SN - 0026-9255
IS - 3
ER -